Functions of Several Variables - Drexel University

MATH 200 WEEK 4 - MONDAY

FUNCTIONS OF SEVERAL VARIABLES

MATH 200

MAIN GOALS FOR TODAY

Be able to describe and sketch the domain of a function of

two or more variables

Domains will be 2D or 3D regions Know how to evaluate a function of two or more variables Be able to compute and sketch level curves & surfaces

These are just traces of the form z = k

MATH 200

EXAMPLES AND NOTATION

The following are all

functions of several variables

f(x,y) = sin(x) + cos(y) g(x,y,z) = xyz z = ln(x2+y2) A = bh/2 V = lwh

MATH 200

DEFINITIONS

A function of two variables, x and y, is a rule that assigns

to each ordered pair, (x,y), exactly one real number.

We assign the value of f(x,y) to z to get a surface

The domain of a function of two variables is the set of

ordered pairs (x,y) for which f is defined

A function of three variables, x, y, and z, is a rule that

assigns to each ordered triple, (x,y,z), exactly one real number.

The domain of a function of three variables is the set of

ordered triples (x,y,z) for which f is defined

MATH 200

DOMAIN FOR A FUNCTION OF TWO VARIABLES

Consider the function

f(x,y) = ln(1-x2-y2)

We know that the input

for ln() must be positive

1 - x2 - y2 > 0

x2 + y2 < 1

Let's sketch the

domain along with the graph of f

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